Chemical reactions underpin the production of pretty much everything in our modern world. But, what is the driving force behind reactions? Why do some reactions occur over geological time scales whilst others are so fast that we need femtosecond-pulsed lasers to study them? Ultimately, what is going on at the atomic level? Discover the answers to such fundamental questions and more on this course in introductory physical chemistry.
The course covers the key concepts of three of the principal topics in first-year undergraduate physical chemistry: thermodynamics, kinetics and quantum mechanics. These three topics cover whether or not reactions occur, how fast they go and what is actually going on at the sub-atomic scale.

Taught By

Patrick J O'Malley, D.Sc

Michael W. Anderson, FRSC

Jonathan Agger, MRSC

Transcript

[BLANK_AUDIO]. Hi there. In this presentation, we're going to look at the solutions of the Schroedinger Equation for hydrogenic atoms system. Now in a previous, in the previous presentation we showed that you could write, in shorter notation, the Schrรถdinger equation for a hydrogenic atom system, as follows. And here what we're using is we're using r theta and, and phi. The spherical coordinate, coordinate system. And we mentioned that you need to transfer to this coordinate system. Because what this enables you to do is it allows you to, if you like, separate the variables, and solve the separate equations for the r component, the radial component, the theta component and the, and the phi component. And we define these in the, the last presentation. Because you can break it down into, as we said, a radial part, or times a function the R, the, the distance of the electron from the central nucleus. And if you multiply that then by an angular term, which we define usually as Y theta psi. Sorry, I meant Y theta phi. So, we're not, you can solve this differential equation that's embedded, if you like, in this equation here. But it's it's quite a difficult solution to do. And we really, it's, it would be an inappropriate use of our time to go in to it in detail in, in this course. And what we're mainly interested in as chemists, is we're interested in these solutions, or the wave functions and the energies that come out in the solutions. So, we're going to, we're going to concentrate on them. Now, first of all like the path in the box, the wave functions are going to have boundary conditions. Our boundary conditions are going to be imposed in the, to obtain the differential equation solutions. And of course, remember from the part in the box, it was these boundary conditions that led to the quantization phenomena. In this case we're talking about a, a three dimensional wave function. So it's a little bit more, more complex. But again, the imposition of the boundary conditions will be what will lead to the quantizations, in other words, the, a ladder of energy levels that will result. So the boundary conditions for the hydrogenic atom systems are that the r can go from zero to infinity, theta can go from 0 to pi as a radiance, and phi can go from 0 up to 2 pi. Now, when we talked about the particle in a box problem, it was a one dimensional problem and if you remember back, we got one quantum number out. And this we called this N and this is an integer going from 1, 2, 3, 4, 5 and so on up. Now because we're talking about a three dimensional problem, we're going to get from this, we're going to get a three quantum numbers. So we're going to get three quantum numbers. Now recall these and you're probably familiar with them from your general chemistry courses, we call them n, l, and m sub L. N, we call the, we call that the principal quantum number. L we are going to call the azimuthal number and mL is the, known as the magnetic quantum number. [SOUND] Now n, the principle quantum number, n can have values ranging from 1, 2, 3, 4, all the way up to infinity, if you want to. And then the L quantum number, called the Azimuthal quantum number, and that's called L. L is equal to 0, 1, 2, 3 and so forth on up to n minus 1. So for a given value of n, there are n allowed values of L. All the values are positive. So, for example, if n is equal to 3. So therefore l for n equals 3 can have values 0, 1, or 2. The other quantum number, mL, and mL can have values, so it can be equal to l, l minus 1, l minus 2, and so forth on up to minus l. And for a given value at l, there are 2 l plus 1 values of m sub l. So these are the three quantum numbers that come out of solutions of the Schrรถdinger equation for the hydrogenic atom system. And in the next presentation we'll move on to talk about the different types of wave functions that come out. [BLANK_AUDIO]

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